The Learn Physics Thread - Space and Time
  • Found a quote on Einstein's thoughts from the man himself.

    "...a paradox upon which I had already hit at the age of sixteen: If I pursue a beam of light with the velocity c (velocity of light in a vacuum), I should observe such a beam of light as an electromagnetic field at rest though spatially oscillating. There seems to be no such thing, however, neither on the basis of experience nor according to Maxwell's equations. From the very beginning it appeared to me intuitively clear that, judged from the standpoint of such an observer, everything would have to happen according to the same laws as for an observer who, relative to the earth, was at rest. For how should the first observer know or be able to determine, that he is in a state of fast uniform motion? One sees in this paradox the germ of the special relativity theory is already contained."
    "Plus he wore shorts like a total cunt" - Bob
  • Hopefully we haven't lost anyone. It's hard to judge so I've taken to over-explaining, especially on how the idea of inertia is tied to everything when it comes to space and time. We'll double down on inertia when it comes to gravity. Inertia never happens to you, it's a thing that you see happening to everyone else and yet everyone is correct and they'd argue it never happens to them either. It's a point of view and the universe respects that.
    "Plus he wore shorts like a total cunt" - Bob
  • It's also interesting how the natural world (physics) encompasses most, if not all the facets of maths.
    Discrete, continue, binary, probability, trigonometry. It's all there and it somehow makes sense?
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  • It's like it's built out of maths, something muzzy strongly disagrees with.
    "Plus he wore shorts like a total cunt" - Bob
  • It wouldn't surprise me if the structure of our universe(s) is a fractal at heart.
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  • davyK
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    There's a chance we will never know how it all works.  Our ability may be limited by the logical and mathematical systems we work in. We may be incapable of working with the systems that are required to figure it all out because of how we perceive the world or the plane of existence we are on.  

    Godel found out that our systems are flawed and maybe that is a fundamental limit showing itself to us.

    Maybe we will one day build something that can think in the way that is required but if we do maybe we won't understand it when it tries to explain it to us.

    Doesn't mean we can't keep striving though. Never say never.  We need to figure out how to travel off this planet in the meantime.
    Holding the wrong end of the stick since 2009.
  • Meh, I think the theory of everything will be mathemathically simpler than we suspect. We'll get there with AI if AI doesn't try to murder us first. Or if humanity doesn't try to murder one another with AI/nukes. Considering how stupid and greedy we are the latter is more likely.

    Don't believe we'll ever get off this planet. We're isolated in space and in time, due to a very narrow and specific set of circumstances/parameters supporting our version of biological life. We can travel for thousands (millions? billions?) of lightyears in any direction and we may never encounter another planet that supports our version of life.
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  • davyK
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    I'm not sure AI which is still based on stuff we already know will make any sort of breakthrough.

    If AI or we do figure it out that may well reveal how we get off the planet.

    A theory of everything could well be very simple when looked at by a higher level of intelligence than we have. We are rats measuring the maze and what it's made of without any idea of what's outside it.

    If we don't figure it all out then we might be able to terraform instead of finding somewhere the same as here. That is more likely to succeed. We could move outward in our solar system before our sun becomes a red giant which would buy us more time.

    With you on our greed based stupidity though.  We don't plan anywhere near far enough ahead to do anything of consequence.  We need to think of doing really big things in a different way because we shackle our efforts by trying to pay for things with money which is only an imaginary thing anyhow.
    Holding the wrong end of the stick since 2009.
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    It's like it's built out of maths, something muzzy strongly disagrees with.

    Do I?
  • We should stop trying to break the planet as for now (forever?) it is our only home.
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  • Also, terraforming sounds nice but humans haven't even figured out their gut microbiome. We're slowly consciously killing the earth's biomes but we're thinking of creating new sustainable biomes in outer space.
    Hmmm....
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  • Imagine there is a fair amount of crossover between the two goals.
  • davyK
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    hunk wrote:
    Also, terraforming sounds nice but humans haven't even figured out their gut microbiome. We're slowly consciously killing the earth's biomes but we're thinking of creating new sustainable biomes in outer space. Hmmm....

    Heh. Aye.

    We may be reduced to constructing habitation somewhere that has ice.  That scale of engineering though is simply beyond us because our obsession with states and the capitalism model that just doesn't support it.  It requires global mobilisation of resources.
    Holding the wrong end of the stick since 2009.
  • Ok, so we have Einstein arguing that all inertial frames really are equal and there's no background space that defines a true speed. This means that all the equations of physics must be valid in all inertial frames - that the equals sign holds, and that includes Maxwell's. Before Maxwell, physics hadn't properly investigated electric charge/magnetism and was more or less about stuff moving and Newton's laws of motion.

    If we observe a physics lab on a train, people appreciated you couldn't really tell that you were moving when you did your motion experiments on the train because the lab was moving along with the physicist (because of inertia) and it gave the illusion, at least to the physicist, that they weren't moving. People really thought it was an illusion the physicist suffered from. But now we had all this charge and magnetism stuff and light popping out of it, and everyone but Einstein assumed these phenomena would break on a moving train/spaceship. If the speed of light was a constant it better bloody well be a constant relative to some other universal constant, and everyone assumed that was absolute space.

    Start thinking that speed is a purely relative concept leads to all sorts of disconcerting thoughts because speed = dist / time, and no physicist was prepared to think they were relative too. They didn't even think about thinking about it. There were a couple of brave mathematicians, notably Lorentz, but no proper scientists believed those fannies anyway. Just because they'd proved that the speed of light is independent from the source by only using a pen and paper didn't mean anything. Frankly, they were getting a bit above their station and they should knuckle down and do actual experiments like real men.

    But in 1905 Einstein didn't care. He wasn't in academia because nobody would have him. He passed his exams but after graduation he couldn't pursue his dream of physics research. Staring into space during lectures and thinking about ground breaking ideas can sometimes give the impression you're a bit of a dimwit, and people thought he was either lazy or stupid. Luckily for us he was forced to take a really boring job at a Swiss patent office. Thank fuck they didn't have the internet back then and his mind was free to wander without doing any experiments. Thought experiments were enough despite what physicists with beards say. So boring was it that all the ideas he'd built up over the years formulated into several but distinct physics-shattering ideas.

    And the one we're concerned about is Maxwell and inertia. Inertia is only a different perception of distance. As per the vid that Liv posted, Jim doesn't see a distance that the audience does because they perceive him as moving and Jim doesn't. For Jim, the light clock is just moving up and down. The audience sees a saw-tooth pattern because relative to them Jim is moving horizontally.

    But crucially, according to Einstein they all see the speed of the beam (c) moving at the same speed. This would not apply if Jim was bouncing a basketball. The audience would see the ball moving faster because they have to add the up and down movement to the horizontal movement they see Jim moving. But if Einstein is right, they both see the path of the beam going at the same speed when it comes to light because that must be a constant in all inertial frames, and both Jim and the audience are.

    So it's the observed distance of the path of the light we have to account for. Jim sees a smaller distance than the audience do but everyone agrees the light is moving at c.

    So what's going on? If speed = dist/ time, then c = dist / time, for the audience and Jim. 

    But if the LHS of the equation is a constant for Jim and the audience (c), yet they both see different distances, we must realise they both experience different times to make the LHS a constant for both parties! Jim and the audience do not agree on what the clock says because they don't agree on the distance the light has traveled.

    With the basketball they don't agree with the distance either but that's fine because they don't agree on the speed, so they're happy to agree the LHS is different and the time part can stay the same for both.
    "Plus he wore shorts like a total cunt" - Bob
  • So we're nearly there when it comes to time dilation. We just need speed = dist / time and Pythagoras, along with a couple of postulates.

    The 2 postulates of special relativity are:

    1. All inertial frames are equal.
    2. The speed of light is constant.

    Only Einstein thought they were true but we could assume they are, what happens if they are, and then actually test it by doing experiments. If we knew about the Michelson-Morley results we'd know they were true because that's what that experiment really proves. M-M were expecting that their experiment would show a difference in c when you're moving towards it or away and assumed their equipment wasn't good enough to detect the difference, so they built better versions. But Einstein didn't need any of that.

    Maxwell showed that light must move at c and as the quote somewhere above, there was nothing in the equations that said it could be viewed as stationary. The hard part for people to wrap their heads around is when looking at a torch in another inertial frame. We can maybe appreciate that Einstein sees his torch not violating Maxwell's equations but they have trouble about thinking about a torch moving towards him.

    We can straighten this out by knowing, thanks to doing some calculus on Maxwell's equations, that the speed of light is independent from the source of the light. So the speed of a torch moving relative to Einstein doesn't come into it. And if Einstein is right then the light is not moving relative to space either. Light is invariant to all motion. The speed of light really is a constant, which is what Maxwell's equations were saying all along, we just didn't believe it. This is a profound thing and it's saying that absolute space cannot exist if the speed of light is the same for all observers. So let's assume it is and see what crazy stuff comes out of it, which can then be tested.

    Einstein was brilliant at thinking about simple experiments that could show profound ideas. They're so simple that many assumed they were some cheap maths trick.

    And his idea is a light clock. Two mirrors with a beam of light bouncing between them. For this we'll assume the light is bouncing up and down relative to the observed motion of the clock (as seen by the audience) because the maths is easier - we can use Pythagoras. We could tilt it in any direction but the maths gets harder.

    And here's the proof. Just remember speed = dist / time, so dist = speed * time. We know this. If you're going 60mph for 2hrs you've gone 120 miles. Fair warning, he's a bit jolly.




    I'd recommend you do this with pen and paper. Follow along pausing the video until you've derived it. It's very satisfying and it'll make you understand the difference between the 2 time terms each observer sees. Plz try it, it's easier than it looks. Just Pythagoras really and a little algebra.

    We'll talk about it when you've done your homework.
    "Plus he wore shorts like a total cunt" - Bob
  • That's the thought experiment? It's almost like...... too simple?
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  • hunk wrote:
    That's the thought experiment? It's almost like...... too simple?

    I think that’s what they all said to Einstein at the time. But he was right.
  • double forum borked post
    "Plus he wore shorts like a total cunt" - Bob
  • The maths is simple but it's being brave enough to state that light is constant for all observers, which is really the idea that things don't move relative to space, itself this abandonment of absolute space. The maths is simple but the consequences seem a bit nuts as we'll see. 

    There's a symmetry to all this. The light clock in the rocket also sees the light clock on Earth moving more slowly, so the astronaut sees the person on Earth's watch moving more slowly and vice versa. How can they both see the other's watch moving more slowly? It must be so if they both see their own light clocks behaving normally. It's not just the clocks, it's all the stuff - brains, watches, light clocks, atoms jiggling etc.

    We'll look at this later. Time dilation leads to length contraction and throwing simultaneity in the bin. The watch paradox btw is called the twin paradox, and then we have to start looking at acceleration and then finally we can move on to GR.
    "Plus he wore shorts like a total cunt" - Bob
  • This is the part to think deeply about.
    So the speed of a torch moving relative to Einstein doesn't come into it. And if Einstein is right then the light is not moving relative to space either. Light is invariant to all motion.
    "Plus he wore shorts like a total cunt" - Bob
  • The speed of light is not relative because there's nothing for it to be relative to. It's not relative to the speed of the emitter and it's not relative to space itself once it's emitted.

    So how do we see light moving from A to B? Because the light doesn't see a distance or a time. You can't MOVE relative to space because space and time ARE relative concepts. Light never sees a distance between A and B because it's frozen in time. There's a beautiful symmetry where we both see different things but everything works out in each frame.

    "Plus he wore shorts like a total cunt" - Bob
  • Ah ok. in that context the ramifications make more sense. Einstein was the first one to consider c a constant.
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  • It gets easier to understand as we go on but at first it's handy to think of it from light's point of view, and we haven't done length contraction yet.

    Light lives in a flat universe because it gets everywhere in zero time and it doesn't even know what distance is. So as far as light is concerned we can never be moving towards or away from it. The symmetry is that we percieve it always at a contant speed whether we're moving towards it or not.
    "Plus he wore shorts like a total cunt" - Bob
  • We need to combine space and time into spacetime and it'll start to become clearer.
    "Plus he wore shorts like a total cunt" - Bob
  • So, we're at the slightly confusing part that all physics students get to when we work out the proof of time dilation. It's just Pythagoras and the hard part is getting all the lengths of the sides of the triangle in terms of d, c and v. If we look at the time dilation equation after doing the maths we get this:

    main-qimg-295f0a3f8bb746752b833d77d779faba

    As per the vid proof, the change in time is the time for a tick of the clock that the observer on Earth sees, and the rest time is the time the person moving with the clock sees. So what happens when the speed of the spaceship is going at the speed of light? Ie, what happens when v = c?

    The equation becomes t' = t / 0. Again, I really recommend deriving the equation yourselves. And when we start dividing by zero we get crazy results like infinity. The observer sees everything in the spaceship frozen in time. The astronaut also sees the Earth frozen in time and we'll worry about this later, but we must think about symmetries a little to sort any confusions out.




    So what have we learnt? That speed between two objects is purely relative. There's no baseline absolute space for everything to be relative to, things are just moving at a relative speed to each other. This must always be respected if speed is relative, so speed has a symmetry. If astronaut A sees astronaut B floating towards them, A and B must agree on their relative speed. This HAS to apply if speed is relative. So what about light? That seems different right? Well the answer is no, relative speed symmetry is still respected and here's why:

    Distance and time are different aspects of the same thing. This seems nuts so lets think about it. If the spacecraft is moving at c as seen by the observer on Earth, the observer sees it frozen in time. The light clock has stopped, everything including the astronaut has stopped.

    The observer concludes that for the astronaut, he's getting everywhere in no time! Doesn't matter how far he goes, he gets there before the light clock has moved. The observer concludes that the astronaut must think he's going at an infinite speed! The observer thinks about this and wonders what things must look like for the astronaut. Well he gets everywhere instantly, so he must see that everything appears the same distance away, and that distance is zero! The observer sees the astronaut having no time and the astronaut (if he had some time) sees the universe as having no thickness, at least in the direction of travel.

    So if the astronaut was heading towards you he wouldn't see the gap and concludes your relative speed to each other is zero because there is no distance between you. This relative speed must be respected for the observer too because speed is relative. The difference is that the observer does see a distance between them and concludes that the astronaut is moving, but this is beside the point. It's only the symmetry of the relative speed that needs to be respected. The gap is merely a point of view. The relative speed is the important thing and they must both conclude there is no relative speed - the speed of ANYTHING moving at c is constant.

    The observer experiences this as light being a constant speed. Anything moving at the speed of light sees no distance because it's living in a 2D universe - it's flat in the direction of travel.

    The speed of light is really nothing to do with light, it's the speed limit of the universe. It's the speed at which the universe becomes flat in the direction of travel, and when it's flat you can't be said to be moving at all. This applies to anything that moves at this speed, including gravitational waves. They move at a constant speed too because they don't see a distance and the symmetry of this relative speed must be respected. We'll look at an example of length contraction next time with some proof that distance is purely a relative concept, and we won't need to do any maths.
    "Plus he wore shorts like a total cunt" - Bob
  • So the conclusion to all of this is that you can't move relative to anything that's moving at the speed of light. Hang on you might say, I can move towards a light beam. The fucker's moving towards me! But you actually can't. If you could you would observe it as coming towards you faster. You can move towards the Sun but you cannot move to towards the light itself. The gap between you and the light beam is merely a point of view and the bias in your inertial frame interprets this as movement.
    "Plus he wore shorts like a total cunt" - Bob
  • Errr..... Ok. Think I'm perfectly willing to accept the concepts but that might need a reread or two to understand them.
  • That’s pretty much were I am too. I read through and go ‘Yep. Got it.’ But then five minutes later I need to read it over again.

    Accepting but not understanding. I need to spend a little time with it before I’ll cross that barrier. But that’s how I always feel about physics stuff.
  • It's best to just think about this stuff in a quiet moment. Next time you're on the toilet don't take your phone in and think about this stuff.
    "Plus he wore shorts like a total cunt" - Bob
  • acemuzzy
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    What about Doppler shift tho eh?

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